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We analyze the ultimate quantum limit on the accessible information for anoptical communication scheme when time bins carry coherent light pulsesprepared in one of several orthogonal modes and the phase undergoes diffusionafter each channel use. This scheme, an example of a quantum memory channel,can be viewed as noisy pulse position modulation (PPM) keying with phasefluctuations occurring between consecutive PPM symbols. We derive a generalexpression for the output states in the Fock basis and implement a numericalprocedure to calculate the Holevo quantity. Using asymptotic properties ofToeplitz matrices, we also present an analytic expression for the Holevoquantity valid for very weak signals and sufficiently strong dephasing when thedominant contribution comes from the single-photon sector in the Hilbert spaceof signal states. Based on numerical results we conjecture an inequality forcontributions to the Holevo quantity from multiphoton sectors which impliesthat in the asymptotic limit of weak signals, for arbitrarily small dephasingthe accessible information scales linearly with the average number of photonscontained in the pulse. Such behaviour presents a qualitative departure fromthe fully coherent case.

Dephasing in coherent communication with weak signal states